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42cf5bc1 1// Created on: 1993-03-10
2// Created by: JCV
3// Copyright (c) 1993-1999 Matra Datavision
5//
6// This file is part of Open CASCADE Technology software library.
7//
8// This library is free software; you can redistribute it and/or modify it under
9// the terms of the GNU Lesser General Public License version 2.1 as published
10// by the Free Software Foundation, with special exception defined in the file
11// OCCT_LGPL_EXCEPTION.txt. Consult the file LICENSE_LGPL_21.txt included in OCCT
12// distribution for complete text of the license and disclaimer of any warranty.
13//
14// Alternatively, this file may be used under the terms of Open CASCADE
15// commercial license or contractual agreement.
16
19
20#include <Standard.hxx>
21#include <Standard_Type.hxx>
22
23#include <Standard_Real.hxx>
24#include <Geom_ElementarySurface.hxx>
25#include <Standard_Boolean.hxx>
26#include <Standard_Integer.hxx>
27class Standard_ConstructionError;
28class Standard_RangeError;
29class gp_Ax3;
30class gp_Sphere;
31class Geom_Curve;
32class gp_Pnt;
33class gp_Vec;
34class gp_Trsf;
35class Geom_Geometry;
36
37
38class Geom_SphericalSurface;
39DEFINE_STANDARD_HANDLE(Geom_SphericalSurface, Geom_ElementarySurface)
40
41//! Describes a sphere.
42//! A sphere is defined by its radius, and is positioned in
43//! space by a coordinate system (a gp_Ax3 object), the
44//! origin of which is the center of the sphere.
45//! This coordinate system is the "local coordinate
46//! system" of the sphere. The following apply:
47//! - Rotation around its "main Axis", in the trigonometric
48//! sense given by the "X Direction" and the "Y
49//! Direction", defines the u parametric direction.
50//! - Its "X Axis" gives the origin for the u parameter.
51//! - The "reference meridian" of the sphere is a
53//! sphere. It is located in the plane defined by the
54//! origin, "X Direction" and "main Direction", centered
55//! on the origin, and positioned on the positive side of the "X Axis".
56//! - Rotation around the "Y Axis" gives the v parameter
57//! on the reference meridian.
58//! - The "X Axis" gives the origin of the v parameter on
59//! the reference meridian.
60//! - The v parametric direction is oriented by the "main
61//! Direction", i.e. when v increases, the Z coordinate
62//! increases. (This implies that the "Y Direction"
63//! orients the reference meridian only when the local
64//! coordinate system is indirect.)
65//! - The u isoparametric curve is a half-circle obtained
66//! by rotating the reference meridian of the sphere
67//! through an angle u around the "main Axis", in the
68//! trigonometric sense defined by the "X Direction"
69//! and the "Y Direction".
70//! The parametric equation of the sphere is:
71//! P(u,v) = O + R*cos(v)*(cos(u)*XDir + sin(u)*YDir)+R*sin(v)*ZDir
72//! where:
73//! - O, XDir, YDir and ZDir are respectively the
74//! origin, the "X Direction", the "Y Direction" and the "Z
75//! Direction" of its local coordinate system, and
76//! - R is the radius of the sphere.
77//! The parametric range of the two parameters is:
78//! - [ 0, 2.*Pi ] for u, and
79//! - [ - Pi/2., + Pi/2. ] for v.
80class Geom_SphericalSurface : public Geom_ElementarySurface
81{
82
83public:
84
85
86
87 //! A3 is the local coordinate system of the surface.
88 //! At the creation the parametrization of the surface is defined
89 //! such as the normal Vector (N = D1U ^ D1V) is directed away from
90 //! the center of the sphere.
91 //! The direction of increasing parametric value V is defined by the
92 //! rotation around the "YDirection" of A2 in the trigonometric sense
93 //! and the orientation of increasing parametric value U is defined
94 //! by the rotation around the main direction of A2 in the
95 //! trigonometric sense.
96 //! Warnings :
97 //! It is not forbidden to create a spherical surface with
99 //! Raised if Radius < 0.0.
100 Standard_EXPORT Geom_SphericalSurface(const gp_Ax3& A3, const Standard_Real Radius);
101
102
103 //! Creates a SphericalSurface from a non persistent Sphere from
104 //! package gp.
105 Standard_EXPORT Geom_SphericalSurface(const gp_Sphere& S);
106
107 //! Assigns the value R to the radius of this sphere.
108 //! Exceptions Standard_ConstructionError if R is less than 0.0.
109 Standard_EXPORT void SetRadius (const Standard_Real R);
110
111 //! Converts the gp_Sphere S into this sphere.
112 Standard_EXPORT void SetSphere (const gp_Sphere& S);
113
114 //! Returns a non persistent sphere with the same geometric
115 //! properties as <me>.
116 Standard_EXPORT gp_Sphere Sphere() const;
117
118 //! Computes the u parameter on the modified
119 //! surface, when reversing its u parametric
120 //! direction, for any point of u parameter U on this sphere.
121 //! In the case of a sphere, these functions returns 2.PI - U.
122 Standard_EXPORT Standard_Real UReversedParameter (const Standard_Real U) const;
123
124 //! Computes the v parameter on the modified
125 //! surface, when reversing its v parametric
126 //! direction, for any point of v parameter V on this sphere.
127 //! In the case of a sphere, these functions returns -U.
128 Standard_EXPORT Standard_Real VReversedParameter (const Standard_Real V) const;
129
130 //! Computes the aera of the spherical surface.
131 Standard_EXPORT Standard_Real Area() const;
132
133 //! Returns the parametric bounds U1, U2, V1 and V2 of this sphere.
134 //! For a sphere: U1 = 0, U2 = 2*PI, V1 = -PI/2, V2 = PI/2.
135 Standard_EXPORT void Bounds (Standard_Real& U1, Standard_Real& U2, Standard_Real& V1, Standard_Real& V2) const;
136
137 //! Returns the coefficients of the implicit equation of the
138 //! quadric in the absolute cartesian coordinates system :
139 //! These coefficients are normalized.
140 //! A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) +
141 //! 2.(C1.X + C2.Y + C3.Z) + D = 0.0
142 Standard_EXPORT void Coefficients (Standard_Real& A1, Standard_Real& A2, Standard_Real& A3, Standard_Real& B1, Standard_Real& B2, Standard_Real& B3, Standard_Real& C1, Standard_Real& C2, Standard_Real& C3, Standard_Real& D) const;
143
144 //! Computes the coefficients of the implicit equation of
145 //! this quadric in the absolute Cartesian coordinate system:
146 //! A1.X**2 + A2.Y**2 + A3.Z**2 + 2.(B1.X.Y + B2.X.Z + B3.Y.Z) +
147 //! 2.(C1.X + C2.Y + C3.Z) + D = 0.0
148 //! An implicit normalization is applied (i.e. A1 = A2 = 1.
149 //! in the local coordinate system of this sphere).
151
152 //! Computes the volume of the spherical surface.
153 Standard_EXPORT Standard_Real Volume() const;
154
155 //! Returns True.
156 Standard_EXPORT Standard_Boolean IsUClosed() const;
157
158 //! Returns False.
159 Standard_EXPORT Standard_Boolean IsVClosed() const;
160
161 //! Returns True.
162 Standard_EXPORT Standard_Boolean IsUPeriodic() const;
163
164 //! Returns False.
165 Standard_EXPORT Standard_Boolean IsVPeriodic() const;
166
167 //! Computes the U isoparametric curve.
168 //! The U isoparametric curves of the surface are defined by the
169 //! section of the spherical surface with plane obtained by rotation
170 //! of the plane (Location, XAxis, ZAxis) around ZAxis. This plane
171 //! defines the origin of parametrization u.
172 //! For a SphericalSurface the UIso curve is a Circle.
173 //! Warnings : The radius of this circle can be zero.
174 Standard_EXPORT Handle(Geom_Curve) UIso (const Standard_Real U) const;
175
176 //! Computes the V isoparametric curve.
177 //! The V isoparametric curves of the surface are defined by
178 //! the section of the spherical surface with plane parallel to the
179 //! plane (Location, XAxis, YAxis). This plane defines the origin of
180 //! parametrization V.
181 //! Be careful if V is close to PI/2 or 3*PI/2 the radius of the
182 //! circle becomes tiny. It is not forbidden in this toolkit to
183 //! create circle with radius = 0.0
184 //! For a SphericalSurface the VIso curve is a Circle.
185 //! Warnings : The radius of this circle can be zero.
186 Standard_EXPORT Handle(Geom_Curve) VIso (const Standard_Real V) const;
187
188
189 //! Computes the point P (U, V) on the surface.
190 //! P (U, V) = Loc + Radius * Sin (V) * Zdir +
191 //! Radius * Cos (V) * (cos (U) * XDir + sin (U) * YDir)
192 //! where Loc is the origin of the placement plane (XAxis, YAxis)
193 //! XDir is the direction of the XAxis and YDir the direction of
194 //! the YAxis and ZDir the direction of the ZAxis.
195 Standard_EXPORT void D0 (const Standard_Real U, const Standard_Real V, gp_Pnt& P) const;
196
197
198 //! Computes the current point and the first derivatives in the
199 //! directions U and V.
200 Standard_EXPORT void D1 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V) const;
201
202
203 //! Computes the current point, the first and the second derivatives
204 //! in the directions U and V.
205 Standard_EXPORT void D2 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV) const;
206
207
208 //! Computes the current point, the first,the second and the third
209 //! derivatives in the directions U and V.
210 Standard_EXPORT void D3 (const Standard_Real U, const Standard_Real V, gp_Pnt& P, gp_Vec& D1U, gp_Vec& D1V, gp_Vec& D2U, gp_Vec& D2V, gp_Vec& D2UV, gp_Vec& D3U, gp_Vec& D3V, gp_Vec& D3UUV, gp_Vec& D3UVV) const;
211
212
213 //! Computes the derivative of order Nu in the direction u
214 //! and Nv in the direction v.
215 //! Raised if Nu + Nv < 1 or Nu < 0 or Nv < 0.
216 Standard_EXPORT gp_Vec DN (const Standard_Real U, const Standard_Real V, const Standard_Integer Nu, const Standard_Integer Nv) const;
217
218 //! Applies the transformation T to this sphere.
219 Standard_EXPORT void Transform (const gp_Trsf& T);
220
221 //! Creates a new object which is a copy of this sphere.
222 Standard_EXPORT Handle(Geom_Geometry) Copy() const;
223
224
225
226
227 DEFINE_STANDARD_RTTI(Geom_SphericalSurface,Geom_ElementarySurface)
228
229protected:
230
231
232
233
234private:
235
236